Random Chain Recurrent Sets for Random Dynamical Systems

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dc.creatorChen, Xiaopeng
dc.creatorDuan, Jinqiao
dc.date2008-10-09
dc.date2009-03-26
dc.date.accessioned2026-07-07T12:56:15Z
dc.date.available2026-07-07T12:56:15Z
dc.descriptionIt is known by the Conley's theorem that the chain recurrent set $CR(ϕ)$ of a deterministic flow $ϕ$ on a compact metric space is the complement of the union of sets $B(A)-A$, where $A$ varies over the collection of attractors and $B(A)$ is the basin of attraction of $A$. It has recently been shown that a similar decomposition result holds for random dynamical systems on noncompact separable complete metric spaces, but under a so-called \emph{absorbing condition}. In the present paper, the authors introduce a notion of random chain recurrent sets for random dynamical systems, and then prove the random Conley's theorem on noncompact separable complete metric spaces \emph{without} the absorbing condition.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/0810.1670
dc.identifierhttp://arxiv.org/abs/0810.1670
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/224519
dc.subjectDynamical Systems
dc.subject37H99, 37B20, 37B25, 37B35
dc.titleRandom Chain Recurrent Sets for Random Dynamical Systems
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